Lecture Notes in Mathematics

Diffeomorphisms of Elliptic 3-Manifolds

Authors: Hong, S., Kalliongis, J., McCullough, D., Rubinstein, J.H.

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About this book

This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle.

The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small list of known exceptions, is contractible. Considerable foundational and background

Table of contents (5 chapters)

  • Elliptic Three-Manifolds and the Smale Conjecture

    Hong, Sungbok (et al.)

    Pages 1-7

  • Diffeomorphisms and Embeddings of Manifolds

    Hong, Sungbok (et al.)

    Pages 9-17

  • The Method of Cerf and Palais

    Hong, Sungbok (et al.)

    Pages 19-51

  • Elliptic Three-Manifolds Containing One-Sided Klein Bottles

    Hong, Sungbok (et al.)

    Pages 53-83

  • Lens Spaces

    Hong, Sungbok (et al.)

    Pages 85-144

Buy this book

eBook $39.95
price for USA (gross)
  • ISBN 978-3-642-31564-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-642-31563-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Diffeomorphisms of Elliptic 3-Manifolds
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2055
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-31564-0
DOI
10.1007/978-3-642-31564-0
Softcover ISBN
978-3-642-31563-3
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 155
Number of Illustrations and Tables
22 b/w illustrations
Topics